# Finding discrete solutions to inequality involving Exponential Integral

I want to identify the least natural number $$n$$ (of course, it suffices to solve this problem for the reals, and then take the floor) such that

$$-c \text{Ei}\left(-e^{\frac{a-d}{c}} (n+1)\right)+a-b (n+1)+c \log (n+1)+\gamma c < 0,$$

where $$\text{Ei}$$ is the exponential integral, $$a,b, c, d$$ are arbitrary real constants, and $$\gamma$$ is the Euler-Mascheroni constant.

I have tried moving the terms around etc., to no avail; Mathematica also does not seem able to solve this.

I was wondering if there are any easy ways to solve this, or at least simplify it?